1
1
Lecture 7:
Topic: Matrices
Reading for this lecture
H&P, Ch 6, Sect 6.3.
Homework for Tutorial in Week 4
Ex 6.3, pp. 248-249, problems 7, 15, 23, 27, 63.
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Conformability for Multiplication
The product,
AB
, of two matrices,
A
and
B
,
exists if, and only if, the number of columns
in
A
equals the number of rows in
B
.
In the following example
AB
exists and has
2 rows and 2 columns.
0
1
2
3 4
5
A
=
6
7
8
9
10
11
B
=
3
The Product of 2 Matrices
The element in the i
th
row and j
th
column of
AB
is the sum of products of elements in the
i
th
row of
A
and the j
th
column of
B
.
0
1
2
3 4
5
6
7
8
9
10
11
AB
=
4
Conformability for Multiplication
The product,
BA
, of two matrices,
A
and
B
,
exists if, and only if, the number of columns
in
B
equals the number of rows in
A
.
In the following example,
BA
exists and has
3 rows and 3 columns.
0
1
2
3 4
5
A
=
6
7
8
9
10
11
B
=
5
The Product of 2 Matrices
0
1
2
3 4
5
6
7
8
9
10
11
BA
=
6
Conformability for Multiplication
If the number of columns in
A
does not equal
the number of rows in
B
then the product,
AB
, of the two matrices does not exist.